A model for gauged skyrmions with low binding energies

Abstract

We consider gauged skyrmions with boundary conditions which break the gauge from SU(2) to U(1) in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge 1 energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.

ADHM skyrmions

“…Constructing the instanton explicitly and solving the equation (2.7) is computationally expensive, and can also be tricky to implement due to the possible appearance of gaugesingularities in the instanton. We can bypass this completely by using a finite-difference approach analogous to one used recently in the context of constructing gauged skyrmions from caloron Nahm data [21]. The approach rests on the fact that the linear map determined by the 2 × 2 complex matrix…”

“…Using ADHM data, calculating the gauge field is non-trivial and it can contain gauge singularities. We bypass both of these issues by generating the Skyrme field using a finite-difference approximation to parallel transport, as recently developed in [21]. This reduces the problem of generating skyrmions from instantons to calculating the kernel of a linear operator, which one can do efficiently.…”